This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Disclaimer: The. exam is a.
SOLMPR, or“)! of problems You wﬁa‘d’
MAT 295 Calculus I ina xamina ion 5“ on M
F .175112004t ‘RM‘ . y Print your name ,. Signature
SU lD number Print your instructor's name Instructions. This examination has 14 problems and 12 printed pages. Make sure your
examination is complete before you begin work. This examination is worth 200 points. The point values are indicated for each of
the problems. Show your work clearly. All answers must bejustified. Calculators may be used
to check your answers, but not tojustify them. Calculators that have symbolic
manipulation capabilities (such as the Tl89 or Tl—92) are prohibited. Do NOT write below this line! l ___ 8h
2.___ 9 __
3.__ 10m
4.___ l l.___
5.___ 12.“
6.___ 13.“ 7 14 Total (l) [12 pts] Given the graph 0ff(x) below. find each of the following limits, if it exists.
If the limit does not exist, write DNE. (3) lim f(x) (b)ﬁp7tX) (c) lim f(x) x—Q‘ (d)INHJKX) 1—»: (2) [16 pts] Evaluate each of the following. Write DNE if the limit does not exist. c 2 .
(a) “er 3"
H0 sm(.r) (b) lim “'10, HIO‘ x—lO . 3x3+100x
(c) lim—2———
X*°‘2x —8x+7 3x—6. .xs7 ~4x+a , x>7 (3) [8 pts] Given f(x) ={ For what value of a isfcontinuous at x=7? Justify your answer completely. Include a sketch of the graph of the function. (4) [10 pts] Using the definition of the derivative, find f'(x) for f(x) = 3x2 —2x (5) [15 pts] Find the equation of the tangent line to the curve 2x2 2 point (1,2). y +4x 3y2 at the (6) [15 pts] A ladder 20 feet long rests against a vertical wall. If the bottom of the
ladder slides away from the wall at a rate of 2 feet per second, how fast is the top of the
ladder sliding down the wall when the bottom of the ladder is 12 feet from the wall? (7) [36 pts] Find the derivative of each of the followin g functions. Do NOT simplify
your answer. I ,_
(b) f(r)=
x +1 (a) y = x+1 2x—3 2 (c) y = sec(5x3) (d) H(x) = cos3(5x) (e) g(x)= .rze3‘ (f) F(.\‘)= I2sin2(l) d!
I 3 4
(8) [8 pts] Using logarithmic differentiation, find the derivative of f(x)= $57:
X + (9) [8 pts] Sketch the graph of a function f(x) having the following characteristics: f(0)=4 andf(6)=0
f'(x)<0 ifx<2 andx>4
f'(2) does not exist f'(4) =0 f(x) >0 if 2 < x < 4
f"(x) < 0 if x # 2 (10) [15 pts] Consider the function f(,\') = 2X3  21x2 — 48x + 6 on the closed interval
[2,6l. Be sure to justify each of your answers! (3) Find the absolute maximum and absolute minimum values of the function on [—2,6] (b) Where on l2,6J do these absolute maximum and minimum values occur? (c) Where on [2.6] is the function increasing? (d) Where on [2,6l is the function concave down? (ll) [15 pts] From an 8 by 15 rectangular piece of posterboard, cut four identical
squares, one in each corner. What size squares should be cut out to achieve the
maximum volume ofthe open box obtained by folding up the sides? Include a carefully labeled diagram as part of your solution. Justify your answer using the
first or second derivative test. (12) [7 pts] Use a Riemann Sum with n=4 subirHervals and right hand endpoints to _ 3
estimate f1 .vzdx. (l3) [7 pts] Find the mean (or average) value of the function f(x) = l9 x] on the closed
interval [6.11l. (14) [28 pts] Evaluate each of the following: (a) fogsin3(x)cos(x)dx (b) f xxgga'x (c) folxx/xz +1 dx (d) f (24‘ +—3— dx ...
View
Full Document
 Spring '11
 NA

Click to edit the document details